During Christmas, Vaidev's candle and Fred's candle were placed on an altar. Vaidev's candle was 15 cm longer than Fred's candle. Vaidev's candle and Fred's candle were lit at 1.00 p.m. and 9.00 p.m. respectively. They burnt down to the same height at 11.00 p.m.. At 4, Fred's candle was burnt out while Vaidev's candle was burnt out at 1. Find the original height of each candle.
(a) Fred's candle
(b) Vaidev's candle
|
Vaidev |
Fred |
Comparing the heights of candles |
15 cm more |
|
1 p.m. |
Lighted |
|
9 p.m. |
|
Lighted |
Burning time to reach same height |
10 h |
2 h |
11 p.m. |
Same height |
4 a.m. |
|
Burnt out |
1.30 a.m. |
Burnt out |
|
Remaining burning time for each candle to burn out |
5 h |
2.5 h |
(a)
After reaching the same height, total remaining burning time for each candle to burn out:
5 hours of Vaidev's candle burning → 2.5 hours of Fred's candle burning
10 hours of Vaidev's candle burning → 5 hours of Fred's candle burning
Time taken for Fred's candle to burn 15 cm in height
= 5 - 2
= 3 h
3 hours of Fred's candle burning → 15 cm
1 hour of Fred's candle burning → 15 ÷ 3 = 5 cm
Total time taken for Fred's candle to burn
= 2.5 + 2
= 4.5 h
4.5 hours of Fred's candle burning
= 4.5 x 5
= 22.5 cm
Original height of Fred's candle = 22.5 cm
(b)
Original height of Vaidev's candle
= 22.5 + 15
= 37.5 cm
Answer(s): (a) 22.5 cm; (b) 37.5 cm